Josiah Willard Gibbs. 193 



account of his natural tendency toward elegance and concise- 

 ness of mathematical method. He did not, however, find in 

 Hamilton's system of quaternions an instrument altogether 

 suited to his needs, in this respect sharing the experience of 

 other investigators who have, of late years, seemed more and 

 more inclined, for practical purposes, to reject the quater- 

 nionic analysis, notwithstanding its beauty and logical com- 

 pleteness, in favor of a simpler and more direct treatment of 

 the subject. For the use of his students. Professor Gibbs 

 privately printed in 1881 and 1881 a very concise account of 

 the vector analysis whicii he had developed, and this pamphlet 

 was to some extent circulated among those especially inter- 

 ested in tlie subject. In the development of this system the 

 author had been led to study deeply the Ausdehnungslehre of 

 Grassmann, and the subject of multiple algebra in general; 

 these investigations interested him greatly up to the time of 

 his death, and he has often remarked that he had more plea- 

 sure in the study of multiple algebra than in any other of his 

 intellectual activities. His rejection of quaternions, and his 

 championship of Grassmann's claim to be considered the 

 founder of modern algebra, led to some papers of a somewhat 

 controversial character, most of which appeared in the columns 

 of " Nature.'' When the utility of his system as an instru- 

 ment for physical research had been proved by twenty years 

 experience of himself and of his pupils. Professor Gibbs con- 

 sented, though somewhat reluctantly, to its formal publication in 

 much more extended form than in the original ]3amplilet. As 

 he was at that time wholly occupied with another work, the 

 task of preparing this treatise for publication was entrusted to 

 one of his students. Dr. E. B. Wilson, whose very successful 

 accomplishment of the work entitles him to the gratitude of 

 all who are interested in the subject. 



The reluctance of Professor Gibbs to publish his system of 

 vector analysis certainly did not arise from any doubt in his 

 own mind as to its utility, or the desirability of its being more 

 widely employed ; it seemed rather to be due to the feeling 

 that it was not an original contribution to mathematics, but 

 was rather an adaptation for special purposes of the work of 

 others. Of many portions of the work this is of course 

 necessarily true, and it is rather by the selection of methods 

 and by systematization of the presentation that the author has 

 served the cause of vector analysis. But in the treatment of 

 the linear vector function and the theory of dyadics to which 

 this leads, a distinct advance was made which was of conse- 

 quence not only in the more restricted field of vector analysis, 

 but also in the broader theory of multiple algebra in general. 



